Question

Problem 11-5 Sensitivity Analysis and Break-Even [LO1, 3]

We are evaluating a project that costs $583,800, has a six-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 90,000 units per year. Price per unit is $41, variable cost per unit is $27, and fixed costs are $695,000 per year. The tax rate is 25 percent, and we require a return of 9 percent on this project.

   

a-1.	Calculate the accounting break-even point. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)
a-2.	What is the degree of operating leverage at the accounting break-even point? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
b-1.	Calculate the base-case cash flow and NPV. (Do not round intermediate calculations. Round your cash flow answer to the nearest whole number, e.g., 32. Round your NPV answer to 2 decimal places, e.g., 32.16.)
b-2.	What is the sensitivity of NPV to changes in the quantity sold? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32. )

Answer 1

Solution:
a-1.	Break-even point          56,593 units
Working Notes:
	Accounting break-even point = (Annual fixed cost + Depreciation)/Contribution margin per unit
	Annual fixed cost = $695,000
	Depreciation = (initial investment/life)
	=$583,800/6
	=97,300
	Contribution margin per unit =selling price per unit - variable cost per unit
		=$41 - $27
		=$14 per unit
	Accounting break-even point = (Annual fixed cost + Depreciation)/Contribution margin per unit
		=($695,000 + $97,300)/$14
		=$792,300/$14
		=56,592.8571428 units
		=56,593 units
a-2.	Degree of operating leverage    8.143
Working Notes:
	Degree of operating leverage at the accounting break-even point
	= Contribution margin /operating income
	=$792300/$97300
	=8.142857143
	=8.143
Notes:
	Contribution margin = Contribution margin per units x break even point
		=$14 x ($792,300/$14)
		=792,300
	operating income = Sales - variable cost -fixed cost
	=($792,300/$14) x (41-27) - 695,000
	=$792,300 -695,000
	=$97300
b-1.	Cash flow                        $448,075
	NPV                               $1,426,227.97
Working Notes:
	Operating cash flows base
	=((price - variable cost) x annual quantity - fixed cost ) x (1- tax rate) +( tax rate x depreciation)
	=(($41 - $27) x 90,000 - 695,000 ) x (1- 0.25) +( 0.25 x 97300)
	=($14 x 90,000 - 695,000 ) x 0.75 +24325
	=565000 x 0.75 + 24325
	=423750 + 24325
	=$448,075
	NPVbase = –Initial investment + operating cash flow x (PVIFA 9%,6)
	NPVbase = –$583,800 + 448,075 x 4.48591859
	NPVbase = –$583,800 + 2010027.9722143
	NPVbase = $1,426,227.9722143
	NPVbase = $1,426,227.97
	PVIFA @ 9% for 1 to 6th is calculated = (1 - (1/(1 + 0.09)^6) ) /0.09 = 4.48591859
b-2.	Sensitivity of NPV to changes in the quantity sold       47.10
Working Notes:
	Sensitivity of NPV to changes in the sales figure = Change in NPV/ changes in the quantity sold
	lets take units changes to 95,000 units from 90,000 units
	Operating cash flows base   at 95000 units
	=((price - variable cost) x annual quantity - fixed cost ) x (1- tax rate) +( tax rate x depreciation)
	=(($41 - $27) x 95,000 - 695,000 ) x (1- 0.25) +( 0.25 x 97300)
	=($14 x 95,000 - 695,000 ) x 0.75 +24325
	=635,000 x 0.75 + 24325
	=476250 + 24325
	=$500,575
	NPVbase = –Initial investment + operating cash flow x (PVIFA 9%,6)
	NPVbase = –$583,800 + $500,575 x 4.48591859
	NPVbase = –$583,800 + 2,245,538.698189
	NPVbase = $1,661,738.698189
	PVIFA @ 9% for 1 to 6th is calculated = (1 - (1/(1 + 0.09)^6) ) /0.09 = 4.48591859
	Sensitivity of NPV to changes in the sales figure = Change in NPV/ Change in sales
		=(NPV at 90,000 - NPV at 95,000)/(90,000 -95,000)
		=($1,426,227.9722143 - $1,661,738.698189)/-5000
		=47.10214519
		= 47.10
c.	sensitivity of OCF to changes in the variable cost figure		-67,500
Working Notes:
	sensitivity of OCF to changes in the variable cost figure
	= Change in operating cash flow / change in variable cost
	=(OCF at $30 - OCF at $27)/(new variable cost - Old variable cost)
	=($245,575 - $448,075) /($30-$27)
	=-$202,500/$3
	= -67,500
	Means increase in $1 of variable cost will decrease OCF by $67,500 or Increases if decrease variable cost per unit by $1.
notes	Let new variable cost per unit = $30 per unit
	OCF at new variable cost $30 per unit
	Operating cash flows base
	=((price - variable cost) x annual quantity - fixed cost ) x (1- tax rate) +( tax rate x depreciation)
	=(($41 - $30) x 90,000 - 695,000 ) x (1- 0.25) +( 0.25 x 97300)
	=($11 x 90,000 - 695,000 ) x 0.75 +24325
	=295000 x 0.75 + 24325
	=221250 + 24325
	=$245,575
Please feel free to ask if anything about above solution in comment section of the question.